Symmetry- and Input-Cluster Synchronization in Networks
Abu Bakar Siddique, Louis Pecora, Joe Hart, Francesco Sorrentino
TL;DR
This paper investigates the stability of various cluster synchronization patterns in networks, revealing that a small set of Lyapunov exponents determines stability, with experimental validation in opto-electronic oscillator networks.
Contribution
It introduces a unified approach to analyze stability of symmetry- and input-cluster synchronization patterns using Lyapunov exponents.
Findings
Stability depends on a small set of Lyapunov exponents.
Applicable to symmetry and input-based clusters.
Experimental verification with opto-electronic oscillators.
Abstract
We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital partitions of the network nodes (symmetry-cluster synchronization) and equitable partitions of the network nodes (input-cluster synchronization.) Our results are verified experimentally in networks of coupled opto-electronic oscillators.
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